Post on 13-Apr-2017
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Scientific Programming Using Excel for Beginners: Newton's Method
byRIZAuddin bin Saian
Faculty of Computer & Mathematical SciencesUniversiti Teknologi MARA (Perlis)
Venue: Lab 1, UiTM Perlis5 February 2016 (Friday)
3pm
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Scientific Programming Using Excel for Beginners: Newton's Method
Problem
• We want to find the root for .
xfy
xfy
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Scientific Programming Using Excel for Beginners: Newton's Method
Objective
• To approximate the root forusing Newton’s method (Newton-Raphson method)– Perform Newton’s method by hand.– Write a VBA code to perform the Newton’s
method.
xfy
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Scientific Programming Using Excel for Beginners: Newton's Method
Newton’s Method
nn
nn xfxfxx
'1
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Scientific Programming Using Excel for Beginners: Newton's Method
Equation of tangent line
nn
nn
n
nnn
nnnn
n
nnnnn
xfxfxx
xfxfxx
xxxfxfxxf
xxxfxfxf
'
'
'0intercept at the 0
'
1
1
1
1
11
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Scientific Programming Using Excel for Beginners: Newton's Method
Initial Guess of x
Actual root
xfy
X
Xx0
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 1
X
Tangent line at x0 = -1
0
001 ' xf
xfxx
X
xfy
x0 x1
Actual root
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 2
x1
Tangent line at x1
1
112 ' xf
xfxx
X X
xfy
x0
Actual root
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Scientific Programming Using Excel for Beginners: Newton's Method
Example: Find the root.
Actual root
X
x0 = -1X
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13 xxxf
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Scientific Programming Using Excel for Beginners: Newton's Method
Initial guess of x 13 xxxf
13'
12
3
xxf
xxxf
1, of guess Initial
0 xx
131
'
2
3
1
xxxx
xfxfxxn
The estimated root,
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 1i x xn+1
0 - 1 -1.5
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 2i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 3i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 4i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 5i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 6i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
5 -1.324717957 -1.324717957 5/2/2016
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 6i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
5 -1.324717957 -1.324717957
STOP!
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Scientific Programming Using Excel for Beginners: Newton's Method
Visual Basic for Application (VBA)Press Alt key and hold. Then, press F11 together to open the VBA Editor.
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Scientific Programming Using Excel for Beginners: Newton's Method
Add new Module5/2/2016
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Scientific Programming Using Excel for Beginners: Newton's Method
Define a function5/2/2016
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 1
• Define function Newton with parameter “x” and return the estimation value for the root of
with x0=-1. 13 xxxf
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 1
• Define function Newton with parameter “x” and return the estimation value for the root of
with x0=-1. 13 xxxf
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Scientific Programming Using Excel for Beginners: Newton's Method
Loop5/2/2016
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 2
• Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations.
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 2
• Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations.
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